On a Runge Theorem over $mathbb{R}_3$

In this paper we investigate a topological characterization of the Runge theorem in the Clifford algebra $ mathbb{R}_3$ via the description of the homology groups of axially symmetric open subsets of the quadratic cone in $mathbb{R}_3$.

Compactness of localization operators on modulation spaces of $omega$-tempered distributions

We give sufficient conditions for compactness of localization operators on modulation spaces $textbf{M}^{p,q}_{m_{lambda}}( mathbb{R}^{d})$ of $omega$-tempered distributions whose short-time Fourier transform is in the weighted mixed space $L^{p,q}_{m_lambda}$ for $m_lambda(x)=e^{lambdaomega(x)}$.